Reduce to lowest terms: $ \dfrac{3}{5} \div \dfrac{3}{2} = {?}$
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{3}{2}$ is $ \dfrac{2}{3}$ Therefore: $ \dfrac{3}{5} \div \dfrac{3}{2} = \dfrac{3}{5} \times \dfrac{2}{3} $ $ \phantom{ \dfrac{3}{5} \times \dfrac{2}{3}} = \dfrac{3 \times 2}{5 \times 3} $ $ \phantom{ \dfrac{3}{5} \times \dfrac{2}{3}} = \dfrac{6}{15} $ The numerator and denominator have a common divisor of $3$, so we can simplify: $ \dfrac{6}{15} = \dfrac{6 \div 3}{15 \div 3} = \dfrac{2}{5} $